The win was Martin's second on the tour.
Martin, 23, finished at 17-under 271.
Charl Schwartzel (68) ended up in second place at 272 and Anders Hansen (68) was third at 274.
Martin closed with five straight pars and held off Schwartzel, his playing partner, who bogeyed No. 17.
Richard Sterne (66), Dale Whitnell (66), Robert Rock (69) and Gareth Maybin (71) all totaled 276 and shared fourth.
Martin, from Malaga, Spain, also won the Open de Portugal in 2007, as an amateur. He was the first amateur to win a European Tour tournament.
"It's an unbelievable feeling," Martin said after his Dunhill victory. "I am so happy and there was so much emotion today."
Although the tournament was played in December, it marked the beginning of the European Tour's 2010 schedule.